It seems more and more likely that the story is set is an alternate timeline. There were no Sentinels in the original trilogy (apart from in the Danger Room in X3, and an icon on Stryker's computer in X2).

So, the past must be a different version of events. Could it not just be another reality where things aren't the same? Does it need a trigger event to make it branch off from normal reality, or could it just exist anyway?

According to the Many Worlds Interpretation - a theory of quantum mechanics: "There is a very large – perhaps infinite – number of universes, and everything that could possibly have happened in our past, but did not, has occurred in the past of some other universe or universes."

I can't see how there could be a trigger event prior to 1973 or surely Wolverine would travel back to that point instead? Unless he and the X-Men are unaware of that earlier trigger point - which would therefore mean they don't completely stop the existence of an anti-mutant threat because they don't eliminate it at source.